Fuel cells are electrochemical devices which can be used to produce electrical energy with high efficiency and in an environmentally friendly manner. Fuel cell technology is considered one of the most promising future forms of energy production.
FIG. 1 shows a fuel cell comprising an anode side 100 and a cathode side 102 and an electrolyte 104 between them. The reactants fed to the fuel cell devices undergo a process in which electrical energy and water are produced as a result of an exothermal reaction. In solid oxide fuel cells (SOFCs), oxygen 106 fed to the cathode side receives an electron from the cathode, that is, is reduced to a negative oxygen ion which travels through the electrolyte to the anode where it combines with the fuel 108 used, producing water and carbon dioxide. Between the anode 100 and the cathode 102 is a separate passage, that is, an external electric circuit 111 through which electrons e—(i.e., an electric current) travel through the load 110 to the cathode.
FIG. 2 shows a SOFC (solid oxide fuel cell) device, which may utilize, for example, natural gas, biogas or methanol or other compounds containing hydrocarbons, as its fuel. The fuel cell device arrangement shown in FIG. 2 comprises plate-like fuel cells, each fuel cell comprising an anode 100 and a cathode 102 as show in FIG. 1, and in FIG. 2 the fuel cells are assembled in stack formation 103 (SOFC stack). The fuel is recirculated in feedback arrangement through the anode sides of the fuel cells.
The fuel cell device arrangement shown in FIG. 2 comprises a fuel heat exchanger 105 and a reformer 107. Heat exchangers are used for controlling the heat balance of the fuel cell process and there may be several of them at different locations in the fuel cell device. The excess heat energy in the recirculated gas is recovered in the heat exchanger for use elsewhere in the fuel cell device or in the district heating network. The heat exchanger recovering the heat may thus be at a different location than that shown in FIG. 2. The reformer is a device which converts fuel, such as natural gas, into a form suitable for fuel cells, that is, for example, into a gas mixture containing one half of hydrogen and the rest methane, carbon dioxide and inert gases. The reformer is not, however, necessary in all fuel cell implementations; untreated fuel may also be fed directly to the fuel cells 103.
Only a part of the fuel burned on the fuel cell 103 anodes 100 is recirculated through the anodes in a feedback arrangement and FIG. 2, therefore, shows diagrammatically the exhaustion 114 of the remainder of the fuel from the anodes 100. By using measurement means 112 (such as, for example, fuel flow meter, current meter and temperature meter), measurements can be carried out for the operation of the SOFC device from the through anode recirculating gas. Control processor 116 is closely related to a reciprocal co-operation with the measurement means 112.
Natural gases such as methane and gases containing higher carbon compounds can be used as fuels in SOFCs. It can be desirable to preprocess such gases before feeding to the fuel cells to prevent carbon formation, i.e., coking. In coking, hydrocarbons decompose thermally and produce carbon which adheres to the surfaces of the fuel cell device and adsorbs on catalysts, such as nickel particles. The carbon produced in coking coats some of the active surface of the fuel cell device, thus significantly deteriorating the reactivity of the fuel cell process. The carbon may even completely block the fuel passage.
Preventing coking can be desirable for ensuring a long service life for the fuel cells. The prevention of coking can also save catalysts, that is, the substances (nickel, platinum, etc.) used in fuel cells for accelerating reactions. Gas preprocessing can require water, which is supplied to the fuel cell device. The water produced in combining the oxygen ion and the fuel, that is, the gas on the anode may also be used in the preprocessing of the gas.
In comparative preprocessing, it can be desirable or necessary to know the composition of the gas recirculated through the anode in feedback arrangement with sufficient accuracy for the preprocessing of the gas to be successful. For example, it can be desirable or necessary to control the oxygen/carbon (O/C) ratio, and to some extent also the hydrogen/carbon (H/C) ratio, to avoid the riskiest reaction environment for carbon formation.
In non-dead-end operated fuel cell systems, the fuel utilization (FU) can be a significant controllable parameter affecting system performance and lifetime. Additionally, in systems involving reforming of hydrocarbon fuels, it can be desirable to keep the system conditions of certain fuel streams sufficient to minimize the risk of carbon formation within the system. A means of minimizing carbon formation is to control oxygen-to-carbon ratio (OC-ratio), hydrogen-to-carbon ratio (HC-ratio) and system temperatures, which all together define the probability for carbon formation in the system. A means to maintain a sufficient OC-ratio and HC-ratio include anode exhaust gas recirculation, fuel reforming by partial oxidation and auxiliary water feed.
As both fuel utilization (FU) information and carbon formation information are cumbersome to determine by means of in-line measurements, they can be determined computationally. In systems where the fuel composition is dependent solely on the inlet streams to the system, calculation of the FU information and carbon formation information is rather straight-forward. However, in systems involving anode recirculation, the FU information and carbon formation information become dependent on the mass flow and composition in the recirculation loop as part of the depleted fuel leaving the fuel cell anodes is returned back to the anode inlet streams. If the system involves anode outward leakage or cross-over leakage from anode to cathode side, which can be the case for many types of high temperature fuel cells, the anode outlet composition, i.e., composition being recirculated, cannot be determined without knowing the recirculation flow and a couple of composition characteristics.
For any given recirculation ratio, i.e., fraction of anode outlet gas being recirculated back to the inlet streams, the atomic flows within the anode circulation loop can be calculated analytically through direct substitution. The molar fractions of the actual gas constituents can be based on the atomic fractions being solved for a given condition. Assuming that the anode outlet composition in the presence of anode catalysts at a high temperature, reaches the corresponding thermal equilibrium composition, the anode outlet composition can hence be solved for said given recirculation ratio. The solving of the thermal equilibrium composition can require the determination of a steam reforming reaction rate satisfying a fourth-grade polynomial, whose coefficients are a function of temperature and the said atomic fractions. If the fuel composition does not reach equilibrium, fuel composition can be determined from kinetic models. Having determined the anode outlet composition, the actual flow in the anode recirculation loop can be calculated using characteristic curves for the anode circulation means (for example pump or ejector), or based on a flow measurement of the circulation flow. This, in turn yields the recirculation ratio for the particular anode outlet composition. If this recirculation ratio equals (by a reasonable margin) the original recirculation ratio used to determine the said composition, a valid solution for the recirculation loop flows and hence FU information and carbon formation information have been found. Otherwise, the calculation is repeated modifying the initial value for the recirculation until a valid solution is found.
The described method for determining the fuel flow compositions involves iteration with multiple nested iteration steps. All together, the finding of a valid solution for recirculation ratio and hence for FU information and carbon formation information may, depending on the system conditions and initial values, involve a considerable amount of floating-point arithmetic operations. In systems with limited computation capacity such as industrial control hardware, the described iteration process may require several seconds to complete. Hence, including the calculation in the cyclic task loop of a fuel cell control system can hamper the overall execution time of the control cycle.
Due to the computation intensity of the described method for accurate determination of fuel compositions, solutions have used simplifying means to reduce the computation need, however sacrificing accuracy and/or versatility. PCT/FI2009/050503 discloses a method where interpolation from a look-up table, with pre-calculated solutions for pre-defined combinations of fuel cell currents, temperatures and flows is used to avoid the need for real-time calculation in determination of recirculation ratio, FU ratio and OC ratio. Although significantly less calculation intensive, the applicability of the method is limited to the pre-defined parameter ranges with a highly limited number of parameters that can be varied in order to keep the size of the look-up table reasonable. For example, in biogas applications where the variable composition of the inlet fuel introduces additional degrees of freedom to the flow conditions within the system, the solution described in PCT/FI2009/050503 can have significant shortcomings.